He was of Irish descent on both sides; his father was Admiral Hercules Robinson, his mother a Miss Wood of Rosmead, County Westmeath, from which he afterwards took his title. Passing from the Royal Military Academy Sandhurst into the 87th Foot, he attained the rank of captain; but in 1846, through the influence of Lord Naas, he obtained a post in the Board of Public Works in Ireland, and subsequently became chief commissioner of fairs and markets. His energy in these positions, notably during the famine of 1848, and the clearness and vigour of his reports, secured for him at the age of thirty the office of president of the island of Montserrat.
Subsequently he was governor of Saint Kitts (1855 - 1859), when he was knighted in recognition of his services in introducing coolie labour into the island; of Hong Kong (5th governor from September 1859 to March 1865); of Ceylon (K.C.M.G in 1869); and of New South Wales (1872 - 1879). It fell to his lot to annex the Fiji Islands to the British Empire, and his services were rewarded in 1875 by promotion to G.C.M.G.
In 1879 he was transferred to New Zealand, and in 1880 he succeeded Sir Bartle Frere as high commissioner of South Africa. He arrived in South Africa shortly before the disaster of Majuba, and was one of the commissioners for negotiating a peace which was personally distasteful to him. It left him with the task of conciliating on the one hand a Dutch party elated with victory, and on the other hand a British party almost ready to despair of the British connexion.
He was called home in 1883 to advise the government on the terms of the new convention concluded with the Transvaal Boers in February 1884. On his return to South Africa he found that a critical situation had arisen in Bechuanaland (today's Botswana), where Boer commandos had seized large tracts of territory and proclaimed the "republics" of Stella and Goshen. They refused to retire within the limits of the Transvaal as defined by the new convention, and Robinson, alive to the necessity of preserving this country — the main road to the north — for Great Britain, determined on vigorous action. John Mackenzie and later Cecil Rhodes were sent to secure the peaceful submission of the Boers, but without immediate result, partly owing to the attitude of the Cape ministry. Robinson's declaration that the advice of his ministers to patch up a settlement with the filibustering Boers was equivalent to a condonation of crime, led to the expedition of Sir Charles Warren and the annexation of Bechuanaland early in 1885. The difficulties of Robinson's position were illustrated by the dispute which arose between him and Warren, who declared that the high commissioner's duties to the home government were at times in conflict with the action which, as governor of Cape Colony, he was bound to take on the advice of his ministers in the interests of the colony. Sir Hercules Robinson succeeded in winning the confidence of President Kruger by his fair-mindedness, while he seconded Rhodes' efforts to unite the British and Dutch parties in Cape Colony. His mind, however, was that of the administrator as distinguished from the statesman, and he was content to settle difficulties as they arose.
In 1886 he investigated the charges brought against Sir John Pope-Hennessy, governor of Mauritius, and decreed his suspension pending the decision of the home authorities, who eventually reinstated Pope-Hennessy. In 1887 Robinson was induced by Rhodes to give his consent to the conclusion of a treaty with Lobengula which secured British rights in Matabele and Mashona lands.
In May 1889 Robinson retired. In his farewell speech he declared that there was no permanent place in South Africa for direct Imperial rule. This was interpreted to mean that South Africa must ultimately become independent — an idea repugnant to him. He explained in a letter to The Times in 1895 that he had referred to the "direct rule of Downing Street over the crown colonies, as contrasted with responsible colonial government." He was made a baronet in 1891. Early in 1895, when he had entered his 71st year and was not in robust health, he yielded to the entreaties of Lord Rosebery's cabinet, and went out again to South Africa, in succession to Sir H. Loch.
His second term of office was not fortunate. The Jameson Raid produced a permanent estrangement between him and Cecil Rhodes, and he was out of sympathy with the new colonial secretary, Joseph Chamberlain, who had criticized his appointment, and now desired Robinson to take this opportunity of settling the whole question of the position of the Uitlanders in the Transvaal. Robinson answered that the moment was inopportune, and that he must be left to choose his own time. Alarmed at the imminent danger of war, he confined his efforts to inducing the Johannesburgers to lay down their arms on condition that the raiders' lives were spared, not knowing that these terms had already been granted to Jameson. He came home to confer with the government, and was raised to the peerage as Baron Rosmead. He returned to South Africa later in the year, but was compelled by ill-health, in April 1897, to quit his post. He died in London, and was succeeded in the title by his son.